A method for non-sequential polarization ray tracing in birefringent media

Abstract

The present invention relates to the technical field of ray tracing, specifically providing a method for tracing non-sequential polarized rays in a birefringent medium. First, the birefringent medium parameters and incident light parameters are determined. Next, the wave vectors and refractive indices of the transmitted and reflected light generated after the incident light enters the birefringent medium are iteratively calculated. Singular value decomposition is then used to calculate the polarization states of the transmitted and reflected light. The propagation directions, Fresnel amplitude coefficients, transmittances, and reflectances of the transmitted and reflected light are further calculated. Finally, the propagation process and optical path length of the incident light are calculated, completing the ray tracing. The method can accurately trace non-sequential polarized rays in a birefringent medium, has strong versatility, and provides highly accurate tracing results.

Description

Technical Field

[0001] The present invention relates to the technical field of ray tracing, and in particular provides a method for tracing non-sequential polarized rays in a birefringent medium. Background Art

[0002] Geometric ray tracing is a fundamental tool for optical system design and analysis. Conventional geometric ray tracing methods currently focus on the propagation, refraction, and reflection of light in isotropic, homogeneous, and optically inactive media. In these media, the refractive index depends solely on the medium itself and is independent of the light's propagation direction and polarization state. Applying Snell's law and Fresnel's transmission and reflection coefficient formulas alone can yield all the information necessary for geometric ray propagation, including ray position, direction, reflectivity and transmittance, and phase variation. Geometric ray tracing does not consider the polarization state of light, and instead averages the energy of the S and P beams after reflection at the surface of the medium and combines them into a single ray for continued tracing.

[0003] Polarization ray tracing and geometric ray tracing belong to sequential ray tracing. On the basis of geometric ray tracing, polarization ray tracing takes into account the polarization state of light, equates the optical element or the surface composed of optical elements to a Jones matrix, and calculates the Jones vector of each light passing through the optical element or the surface composed of optical elements, thereby calculating polarization aberrations such as bidirectional attenuation and phase delay.

[0004] Many optical systems contain anisotropic or optically active materials, such as liquid crystals, wave plates, filters, and some glasses for ultraviolet applications. These materials are called birefringent materials. Birefringent materials include uniaxial, biaxial, or optically active crystals. In these materials, the refractive index depends not only on the direction of light propagation but also on its polarization state. When light strikes a birefringent material, it typically splits into two rays with different refractive indices and polarization states, a phenomenon known as birefringence. When light strikes a surface formed by a birefringent medium, four possible modes of light may be generated.

[0005] Existing polarization ray tracing methods do not consider the propagation, refraction, and reflection behavior of polarized light in anisotropic, optically active media. Even if a birefringent medium such as a quarter-wave plate exists in the optical system, the polarization ray tracing method only equates it to a Jones matrix or a Mueller matrix, and cannot simulate the propagation, refraction, and reflection behavior of polarized light in anisotropic, optically active media. Summary of the Invention

[0006] To solve the above problems, the present invention provides a method for tracing non-sequential polarized light in a birefringent medium, which completes the tracing by iteratively calculating the wave vector and refractive index of the transmitted light and the reflected light, and calculating the polarization state of the transmitted light and the reflected light using singular value decomposition.

[0007] The present invention provides a method for tracing non-sequential polarized light in a birefringent medium, comprising:

[0008] S1: Based on the birefringent medium parameters and the incident light parameters, iteratively calculate the wave vector and refractive index of the transmitted light and reflected light generated after the incident light enters the birefringent medium;

[0009] The iterative calculation process is:

[0010] S1.1: Selecting the Refractive Index As an initial estimate, is the x-axis principal dielectric constant of the medium where the light to be calculated is located;

[0011] S1.2: Calculate the bias constant ;

[0012] S1.3: Based on the bias constant , calculate the wave vector in the global coordinate system ;

[0013] S1.4: Calculate the wave vector in the global coordinate system Projection of the crystal optical axis in the local coordinate system ;

[0014] S1.5: Construct about The quadratic equation of

[0015] S1.6: Solved The new value of , which is a positive number;

[0016] S1.7: Repeat steps S1.2 to S1.6 until Convergence, when the refractive index Stable to If it is within , it is considered convergent;

[0017] S2: Calculate the polarization state of the transmitted and reflected light using singular value decomposition;

[0018] S3: Calculate the propagation direction of transmitted light and reflected light;

[0019] S4: Calculate the Fresnel amplitude coefficient of transmitted light and reflected light, and calculate the transmittance or reflectance;

[0020] S5: Calculate the propagation process and optical path of the incident light.

[0021] Preferably, the birefringent medium parameters include the surface normal direction, the dielectric constant of the birefringent medium on both sides of the birefringent surface, and the optical rotation in the global coordinate system. axis, axis, The components on the axis, the dielectric tensor and optical rotation tensor in diagonal form in the local coordinate system of the crystal optical axis; the incident light parameters include the normalized three-dimensional Jones vector corresponding to the incident light in the global coordinate system, the normalized wave vector corresponding to the incident light, the normalized propagation direction of the incident light corresponding to the incident light, and the refractive index of the birefringent medium on the incident side.

[0022] Preferably, about The quadratic equation expression is:

[0023] ;

[0024] in,

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] 、 、 Indicates that in the global coordinate system, the optical rotation is axis, axis, The component on the axis, 、 、 represents the principal dielectric constant of the birefringent medium on both sides of the birefringent surface, Represents wave vector projection In the local coordinate system of the crystal optical axis, the components on the x-axis, y-axis and z-axis, respectively, in transmission mode, and Indicates the dielectric constant and optical rotation of the birefringent medium on the transmission side, in reflection mode and It represents the electric constant and optical rotation of the birefringent medium on the reflection side.

[0030] Preferably, the singular value decomposition calculation process is: construct the process matrix and matrix , perform singular value decomposition:

[0031] ;

[0032] ;

[0033] in, represents the optical rotation tensor of the birefringent medium on the transmission side, is the dielectric tensor in the global coordinate system. For the reflection mode, the subscript Need to be replaced with , and Both represent unitary matrices, Diagonal matrix.

[0034] Preferably, the light propagation direction for:

[0035] ;

[0036] in, represents the normalized electric field vector, represents the normalized magnetic field polarization state, and * represents the complex conjugate.

[0037] Preferably, the Fresnel amplitude coefficient for:

[0038] ;

[0039] in, and represents the tangent vector, , , represents the normalized electric field vector of the incident light, represents the normalized magnetic field polarization state of the incident light.

[0040] Preferably, the calculation formulas for transmittance and reflectance are:

[0041] ;

[0042] in, is the angle between the calculated light and the surface normal, The value is , represents the angle between the incident light and the surface normal, represents the refractive index of the outgoing light, Represents the refractive index of the birefringent medium on the incident side.

[0043] Preferably, the optical path for:

[0044] ,

[0045] in, Represents the cosine of the angle between the wave vector and the light propagation direction vector, represents the geometric length, Represents the refractive index.

[0046] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0047] While this method is designed for media with anisotropic or optically active materials on both sides of the surface, it is equally applicable to isotropic and non-optically active media. For isotropic media, the method can be directly applied by setting the elements of the diagonalized dielectric tensor equal. For non-optically active media, the method can be directly applied by setting the optical rotation tensor G to zero. Furthermore, this framework can also be used for polarized ray tracing through absorptive, dichroic, or magneto-optical media (such as Faraday media). Therefore, the method is applicable to nearly all linear, homogeneous optical materials and uniaxial thin films, making it highly versatile.

[0048] The basic steps of the ray tracing method of the present invention and the polarization ray tracing and geometric ray tracing methods are the same in all media. The only difference is that when solving the refraction problem of the medium surface, the relationship between the refractive index and the propagation direction of the wave vector is different. Therefore, the method of the present invention has good compatibility with existing optical design software, and many existing related optical design algorithms can continue to be used.

[0049] The proposed method expands the range of materials and optical systems that can be analyzed, enabling optical designers to analyze the effects of polarization components in optical systems. Furthermore, optical designers can use the proposed method to optimize existing birefringent components or design entirely new ones. The proposed method will provide a deeper understanding of the performance and limitations of optical systems containing birefringent components. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a flow chart of a method for non-sequential polarization ray tracing in a birefringent medium provided according to an embodiment of the present invention;

[0051] Figure 2 It is a light propagation path diagram of a simulation experiment provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation to the present invention. Similar elements in different embodiments use associated similar element numbers. In the following embodiments, many detailed descriptions are intended to enable the present invention to be better understood. However, those skilled in the art can easily recognize that some of the features can be omitted in different situations, or can be replaced by other elements, materials, or methods. In some cases, some operations related to the present invention are not shown or described in the specification. This is to avoid the core part of the present invention being overwhelmed by too much description. For those skilled in the art, it is not necessary to describe these related operations in detail. They can fully understand the related operations based on the description in the specification and the general technical knowledge in the art.

[0053] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments of the present invention can be combined with each other to form various implementation methods. At the same time, the steps or actions in the method description can also be interchanged or adjusted in a manner that is obvious to those skilled in the art. Therefore, the various orders in the description and the drawings are only for the purpose of clearly describing a certain embodiment and are not intended to be a required order, unless otherwise specified that a certain order must be followed.

[0054] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0055] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art can understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0056] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0057] Non-sequential polarization ray tracing is a key technology used in optical design simulation to analyze the propagation of polarized light in complex optical systems. Its core lies in simulating light passing through optical elements in an arbitrary order and tracking the changes in polarization state. The tracing results require the acquisition of the following light propagation data: light refractive index, transmittance or reflectivity (transmitted light requires transmittance, reflected light requires reflectivity), propagation direction, wave vector, Jones vector, and optical path length. Birefringent medium is an anisotropic material or optically active material. Two birefringent media are bonded together to form a birefringent surface. When the incident light enters the birefringent surface, four outgoing lights are generated, such as Figure 1 and Figure 2 As shown, the embodiment of the present invention provides a method for tracing non-sequential polarized rays in a birefringent medium in response to the above-mentioned light propagation situation, which is specifically as follows:

[0058] S1: Based on the birefringent medium parameters and the incident light parameters, iteratively calculate the wave vector and refractive index of the transmitted light and reflected light generated after the incident light enters the birefringent medium.

[0059] The birefringent surface is formed by two birefringent media. Before ray tracing, the medium parameters of the two birefringent media and the incident light parameters need to be confirmed. The parameters represent the relevant parameters of the birefringent medium on the transmission side. It should be noted that along the direction of light propagation, the surface of the medium; the subscript is Parameters represent parameters related to the incident light, for example, parameters related to the incident light or parameters related to the medium on the incident side. and No actual meaning, only represents a variable. The value is When , it indicates transmission mode; when The value is When , it indicates the reflection mode. The value is When the birefringent medium is a uniaxial crystal, it indicates the normal mode. If the birefringent medium is a biaxial crystal, it indicates the fast light mode. The refractive index of the birefringent medium is Smaller; when The value is When the crystal is uniaxial, it indicates the anomalous mode, and when the crystal is biaxial, it indicates the slow light mode. The refractive index of the birefringent medium is Larger.

[0060] The input incident light parameters are: the normalized three-dimensional Jones vector corresponding to the incident light in the global coordinate system , the normalized wave vector corresponding to the incident light , the propagation direction of the normalized incident light corresponding to the incident light , the refractive index of the birefringent medium on the incident side .in, 、 and They represent the Jones vector of the incident light in global coordinates. exist axis, axis, Components on the axis.

[0061] Input birefringent medium parameters on both sides of the birefringent surface are: surface normal direction ; The principal dielectric constant of the birefringent medium on both sides of the birefringent surface , , ,in, 、 and They represent the principal refractive index of the medium in the global coordinate system, and the x, y, and z axes are the principal dielectric axes of the medium; in the global coordinate system, the optical rotation is axis, axis, The components on the axis are 、 and ; In the local coordinate system of the crystal optical axis, the diagonal form of the dielectric tensor is , the optical rotation tensor is , where the main dielectric constant is 、 、 is the element in the matrix corresponding to the dielectric tensor, the optical rotation 、 、 is the element in the matrix corresponding to the optical rotation tensor. and optical rotation tensor After matrix transformation, the dielectric tensor in the global coordinate system can be obtained and optical rotation tensor .

[0062] In optical design programs, the matrix and It only needs to be calculated once before each ray tracing and stored in the extended glass database. It should be noted that the local coordinate system of the crystal optical axis is set by the user according to the actual situation when applying the method of the present invention.

[0063] Iteratively calculates the wave vector and refractive index of the transmitted and reflected light generated by the incident light entering the birefringent medium. When any beam of light is incident on a birefringent surface, it may produce , , , There are four types of emitted light. It is the refractive index of the birefringent medium on the incident side. However, since the refractive index depends on the propagation direction and polarization state of the light, the actual refractive index of the light needs to be calculated and stored separately.

[0064] The wave vectors of the four outgoing lights are 、 、 、 and the corresponding refractive index 、 、 、 Perform iterative calculation. Since the iterative calculation method is the same, the embodiment of the present invention only describes the iterative calculation method once. During the iteration process, no subscript is used to limit the letters. For example, express 、 、 、 Any one of them. Wave vector It is only an intermediate quantity and is not equivalent to the direction of light propagation. The direction of light propagation is used to trace the light to the next surface. When tracing, the direction of light propagation needs to be solved. , the refractive index of the outgoing light It is determined by an iterative method, the calculation process is complex, and no closed-form analytical solution can be obtained during the derivation process.

[0065] The iterative calculation process is as follows:

[0066] S1.1: Selection As an initial estimate, is the x-axis principal dielectric constant of the medium where the light is to be calculated. For example, when calculating transmitted light, , when calculating reflected light, ,in, and are the refractive indices of transmitted light and reflected light, respectively. It represents the principal dielectric constant of the medium on the x-axis on the transmission side, It represents the principal dielectric constant of the medium along the x-axis on the incident side.

[0067] It should be noted that the refractive index in this formula is , which can be transformed into 、 、 or , corresponding to the four emitted light rays,

[0068] S1.2: Calculate the bias constant , the deflection constant of the transmission mode and the deflection constant of the reflection mode Calculate according to the following formulas:

[0069] ,

[0070] .

[0071] S1.3: Based on the deflection constant calculated in step S1.2 , calculate the wave vector in the global coordinate system :

[0072] .

[0073] S1.4: Calculate the wave vector in the global coordinate system Projection of the crystal optical axis in the local coordinate system :

[0074] ,

[0075] in, is an orthogonal matrix associated with the coordinate system transformation.

[0076] S1.5: Construct about The quadratic equation of :

[0077] ;

[0078] in,

[0079] ;

[0080] ;

[0081] ;

[0082] ;

[0083] Represents wave vector projection In the local coordinate system of the crystal optical axis, the components on the x-axis, y-axis and z-axis, respectively, in transmission mode, and Indicates the dielectric constant and optical rotation of the birefringent medium on the transmission side, in reflection mode and It represents the electric constant and optical rotation of the birefringent medium on the reflection side.

[0084] S1.6: Solving for the Refractive Index The new value of , which should be a positive number. No. Applicable to Light mode, i.e. normal mode or fast light mode, No. Applicable to Light mode, also known as abnormal mode or slow light mode:

[0085] ,

[0086] .

[0087] S1.7: Repeat steps S1.2 to S1.6 until Convergence, when the refractive index Stable to If the value is within , it is considered convergent. The final calculated wave vector and refractive index For refracted light Light, Wave vector and refractive index of light or reflected light Light, Light wave vector and refractive index.

[0088] The calculation process usually does not exceed three iterations to converge. Can be stabilized to When any ray of light is incident on a birefringent surface, it is possible to produce , , , There are 4 modes of light in total, and each mode should be iterated through steps S2.1 to S2.7.

[0089] It is worth noting that the wave vector and refractive index contains square root operations, so a flag should be set. If the wave vector and refractive index If a complex number appears, it means that in this mode, the light is an evanescent wave and will not propagate to the next interface. However, its polarization state still needs to be calculated in order to derive the Fresnel amplitude coefficient.

[0090] S2: Calculate the polarization state of the transmitted and reflected light using singular value decomposition.

[0091] First construct four process matrices :

[0092] ,

[0093] in, Represents the wave vector In the global coordinate system, the components on the x-axis, y-axis, and z-axis, respectively, Subscript Replace with , , , Four matrices are obtained, corresponding to the four rays leaving the interface.

[0094] Construction process matrix :

[0095] ,

[0096] in, is the dielectric tensor in the global coordinate system. For the reflection mode, the subscript Need to be replaced with ,Right now .

[0097] Pair Matrix Perform singular value decomposition:

[0098] ,

[0099] in, and Both represent unitary matrices, Diagonal matrix, the above three matrices are mathematical quantities of the singular value decomposition process.

[0100] Normalize the result to get the vector ,matrix The last column element of is the vector , is the electric field vector, thus determining the electric field polarization state of each mode, and the normalized calculation is as follows:

[0101] .

[0102] It should be noted that the electric field vector , which can be transformed into 、 、 or , corresponding to the four emitted rays, the corresponding calculations obtain the normalized electric field vectors of the four rays respectively: 、 、 or In the embodiment of the present invention, the electric field vector, the electric field polarization state and the Jones vector are the same concepts.

[0103] S3: Calculate the propagation direction of transmitted light and reflected light.

[0104] When calculating the propagation direction of light and the Fresnel amplitude coefficient, the magnetic field corresponding to various modes is also required. The modes mentioned here include not only the normal mode, fast light mode, abnormal mode, and slow light mode described in step S1, but also the incident mode. The incident mode can be understood as the incident light. Here, it refers to calculating the magnetic field polarization state of the incident light. Calculate the magnetic field polarization state corresponding to the normal mode and fast light mode in reflection and , calculate the magnetic field polarization state corresponding to the abnormal mode and slow light mode in transmission and , calculate the magnetic field polarization state of the incident mode , the calculation method is as follows:

[0105] ,

[0106] .

[0107] in, represents the normalized magnetic field polarization state of the incident light, represents the optical rotation tensor of the birefringent medium on the transmission side, represents the optical rotation tensor of the birefringent medium on the incident side. It should be noted that this formula Transformable into 、 、 or , respectively corresponding to the four emitted light rays, the corresponding calculations are used to obtain the magnetic field polarization states of the four rays. When calculating, , which can be transformed into 、 、 or , corresponding to the four emitted light rays.

[0108] Then calculate the normalized light propagation direction of the four outgoing rays , also known as the Poynting vector:

[0109] ,

[0110] The direction of light propagation is a vector, which can be transformed into 、 、 or , each contains three elements, the corresponding vector The elements of are in the global coordinate system, vector Components on the x-axis, y-axis, and z-axis, vector The components on the x-axis, y-axis, and z-axis are transmission and reflection Light and The direction cosine of the propagation direction of light, * represents the complex conjugate, represents the normalized electric field vector, represents the normalized magnetic field polarization state. The solution for all four outgoing rays is described simultaneously because the calculation of the Fresnel amplitude coefficient requires information about the electromagnetic polarization of all four modes. If a ray is not of interest, it can be omitted from the tracing to the next surface.

[0111] It should be noted that the direction of light propagation in this formula is Transformable into 、 、 or , when calculating, the normalized electric field vector , which can be transformed into 、 、 or , corresponding to the four emitted light rays, in this formula , which can be transformed into 、 、 or , corresponding to the four emitted light rays.

[0112] S4: Calculate the Fresnel amplitude coefficient, transmittance, and reflectance of transmitted and reflected light.

[0113] Define the tangent vector and :

[0114] ;

[0115] .

[0116] if , then select ,in is any direction not parallel to the surface normal The unit vector of .

[0117] Calculate the matrix :

[0118] .

[0119] Calculate the Fresnel amplitude coefficient :

[0120] .

[0121] in, represents the normalized electric field vector of the incident light.

[0122] The transmittance of transmitted light or the reflectance of reflected light is calculated as:

[0123] ,

[0124] in, Represents the angle between the calculated light and the surface normal, The value is , represents the calculated Fresnel amplitude coefficient, Represents the angle between the incident light and the surface normal. It should be noted that in this formula, , which can be transformed into 、 、 or , corresponding to the four emitted light rays, respectively, 、 and There are four corresponding deformations and four types of output light. When the corresponding output light is transmitted light, the calculated value is the transmittance. When the corresponding output light is reflected light, the calculated value is the reflectance, with two types each of reflected light and transmitted light.

[0125] S5: Calculate the light propagation process and optical path.

[0126] After calculating the direction of the light after leaving the current surface, it is necessary to propagate it to the next surface and calculate the light path. If the intersection point of the light at the current surface is , and its refracted light vector is , then it is connected to the next surface The intersection point is , the optical path can be calculated by geometric ray tracing.

[0127] First calculate the geometric length :

[0128] .

[0129] Then calculate the optical path:

[0130] .

[0131] in, It is the cosine of the angle between the wave vector and the direction vector of the light propagation.

[0132] While this method is designed for media with anisotropic or optically active materials on both sides of the surface, it is equally applicable to isotropic and non-optically active media. For isotropic media, the method can be directly applied by setting the elements of the diagonalized dielectric tensor equal. For non-optically active media, the method can be directly applied by setting the optical rotation tensor G to zero. Furthermore, this framework can also be used for polarized ray tracing through absorptive, dichroic, or magneto-optical media (such as Faraday media). Therefore, the method is applicable to all linear, homogeneous optical materials and uniaxial thin films, demonstrating its versatility.

[0133] The basic steps of the ray tracing method of the present invention are the same as those of the polarization ray tracing method and the geometric ray tracing method in all media. The only difference is that when solving the refraction problem of the medium surface, the relationship between the refractive index and the propagation direction of the wave vector is different. Therefore, the method of the present invention has good compatibility with existing optical design software, and many existing related optical design algorithms can continue to be used, such as the Jones matrix, the Mueller matrix, the polarization-dependent point spread function (PSF), and the modulation transfer function (MTF).

[0134] The method proposed in the present invention expands the range of materials and optical systems that can be analyzed, allowing optical designers to analyze the effects of polarization elements in optical systems. For example, the method proposed in the present invention can be used to accurately determine the aberrations of retarders and astigmatism in non-collimated light. In addition, optical designers can use this method to optimize existing birefringent elements or design completely new birefringent elements. For example, the quartz optical rotation lens in an interferometer is used to generate two wavefronts with different curvatures. When the quartz lens is irradiated with linearly polarized light, since it has slightly different focal lengths for right-handed and left-handed circularly polarized light, the wavefronts of the transmitted light beams will have different curvatures. The method of the present invention can calculate the aberrations of these light beams. In short, the method proposed in the present invention will help to gain a deeper understanding of the performance and limitations of optical systems containing birefringent elements.

[0135] To verify the effectiveness of the method of the present invention, the following simulation experiments were conducted on the method of the embodiment of the present invention:

[0136] Simulation conditions:

[0137] In this embodiment of the present invention, a uniaxial crystal is used as a birefringent medium. On a PC with an Intel(R) CPU i7-12700KF and 32GB of memory, the MATLAB R2024a platform is used to simulate the refraction and reflection of a single ray incident on an interface with quartz crystals on both sides. Figure 2 As shown, the wave vector is The light is incident from air into two 6mm thick quartz slices whose crystal optical axis is rotated 60° clockwise around the x-axis and y-axis of the global coordinate system. The refractive index of quartz is , , , , here, Indicates normal mode, Indicates abnormal mode, the propagation direction is of When light is incident on the interface with quartz crystals on both sides, it splits into Four rays of light.

[0138] In the embodiment of the present invention, the normalized three-dimensional Jones vector of the incident light is set The value of the wave vector is The propagation direction is The refractive index is .

[0139] In the embodiment of the present invention, the surface normal direction is set , the refractive index of the birefringent medium on the incident side of the incident light , , the optical rotation of the birefringent medium on the incident side of the incident light , , the optical axis of the birefringent medium on the incident side rotates 60° clockwise around the x-axis of the global coordinate system. The optical axis of the birefringent medium on the transmission side rotates 60° clockwise around the y-axis of the global coordinate system. The rest of the properties are the same as those of the birefringent medium on the incident side.

[0140] Attachment Figure 2 in Indicates the optical axis direction of the left medium, Indicates the direction of the optical axis of the medium on the right.

[0141] Simulation results:

[0142] Tables 1 through 3 show the tracing results of light rays entering a thin quartz crystal slice using the method of an embodiment of the present invention. These data include the light's refractive index, transmission / reflectivity, propagation direction, wave vector, Jones vector, and optical path length. The data in Tables 1 through 3 demonstrate that the method of the present invention effectively simulates the refraction and reflection behavior of light rays in a birefringent, optically active crystal.

[0143] Table 1 Results of the first refraction tracing

[0144]

[0145] Table 2 Results of the second refraction tracing

[0146]

[0147] Table 3 Reflection tracing results

[0148]

[0149] Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art may make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

[0150] The above specific embodiments of the present invention do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the scope of protection of the claims of the present invention.

Claims

1. A method for non-sequential polarization ray tracing in a birefringent medium, characterized in that: include: S1: Iteratively calculating the wave vector and refractive index of the transmitted light and the reflected light generated after the incident light enters the birefringent medium according to the birefringent medium parameters and the incident light parameters; The iterative calculation process is: S1.1: Selecting the Refractive Index As an initial estimate, is the x-axis principal dielectric constant of the medium where the light to be calculated is located; S1.2: Calculate the bias constant ; S1.3: According to the bias constant , calculate the wave vector in the global coordinate system ; S1.4: Calculate the wave vector in the global coordinate system Projection of the crystal optical axis in the local coordinate system ; S1.5: Construct about The quadratic equation of S1.6: Solved The new value of , which is a positive number; S1.7: Repeat steps S1.2 to S1.6 until Convergence, when the refractive index Stable to If it is within , it is considered convergent; S2: Calculating the polarization states of the transmitted light and the reflected light using singular value decomposition; S3: Calculating the propagation directions of the transmitted light and the reflected light; S4: Calculate the Fresnel amplitude coefficient of transmitted light and reflected light, and calculate the transmittance or reflectance; S5: Calculate the propagation process and optical path of the incident light.

2. The method for non-sequential polarization ray tracing in a birefringent medium according to claim 1, wherein: The birefringent medium parameters include the surface normal direction, the dielectric constant of the birefringent medium on both sides of the birefringent surface, the optical rotation in the global coordinate system, axis, axis, The components on the axis, the dielectric tensor and the optical rotation tensor in diagonal form in the local coordinate system of the crystal optical axis; the incident light parameters include the normalized three-dimensional Jones vector corresponding to the incident light in the global coordinate system, the normalized wave vector corresponding to the incident light, the normalized propagation direction of the incident light corresponding to the incident light, and the refractive index of the birefringent medium on the incident side.

3. The method for non-sequential polarization ray tracing in a birefringent medium according to claim 1, wherein: Said about The quadratic equation expression is: ； in, ； ； ； ； 、 、 Indicates that in the global coordinate system, the optical rotation is axis, axis, The component on the axis, 、 、 represents the principal dielectric constant of the birefringent medium on both sides of the birefringent surface, Represents wave vector projection In the local coordinate system of the crystal optical axis, the components on the x-axis, y-axis and z-axis, respectively, in transmission mode, and Indicates the dielectric constant and optical rotation of the birefringent medium on the transmission side, in reflection mode and It represents the electric constant and optical rotation of the birefringent medium on the reflection side.

4. The method for non-sequential polarization ray tracing in a birefringent medium according to claim 1, wherein: The singular value decomposition calculation process is: construct the process matrix and matrix , perform singular value decomposition: ； ； in, represents the optical rotation tensor of the birefringent medium on the transmission side, is the dielectric tensor in the global coordinate system. For the reflection mode, the subscript Need to be replaced with , and Both represent unitary matrices, Diagonal matrix.

5. The method for non-sequential polarization ray tracing in a birefringent medium according to claim 1, wherein: The direction of light propagation for: ； in, represents the normalized electric field vector, represents the normalized magnetic field polarization state, and * represents the complex conjugate.

6. The method for non-sequential polarization ray tracing in a birefringent medium as claimed in claim 1, wherein: The Fresnel amplitude coefficient for: ； in, and represents the tangent vector, , , represents the normalized electric field vector of the incident light, represents the normalized magnetic field polarization state of the incident light.

7. The method for non-sequential polarization ray tracing in a birefringent medium according to claim 1, wherein: The calculation formulas for the transmittance and reflectance are: ； in, is the angle between the calculated light and the surface normal, The value is , represents the angle between the incident light and the surface normal, represents the refractive index of the outgoing light, Represents the refractive index of the birefringent medium on the incident side.

8. The method for non-sequential polarization ray tracing in a birefringent medium as claimed in claim 1, wherein: The optical path for: ， in, Represents the cosine of the angle between the wave vector and the light propagation direction vector, represents the geometric length, Represents the refractive index.

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